Differential Equations for Carrollian Amplitudes

TL;DR

This paper derives and analyzes linear differential equations governing Carrollian MHV gluon and graviton amplitudes, providing new solutions and consistency checks within the framework of Carrollian conformal field theories related to flat spacetime holography.

Contribution

It introduces the first derivation of differential equations for Carrollian amplitudes and finds explicit non-distributional solutions, advancing the understanding of Carrollian CFTs in holography.

Findings

Derived linear differential equations for Carrollian MHV amplitudes

Obtained explicit non-distributional solutions for gluon and graviton cases

Performed consistency checks confirming compatibility with Carrollian symmetries

Abstract

Differential equations are powerful tools in the study of correlation functions in conformal field theories (CFTs). Carrollian amplitudes behave as correlation functions of Carrollian CFT that holographically describes asymptotically flat spacetime. We derive linear differential equations satisfied by Carrollian MHV gluon and graviton amplitudes. We obtain non-distributional solutions for both the gluon and graviton cases. We perform various consistency checks for these differential equations, including compatibility with conformal Carrollian symmetries.